CBSE Class 12 Sample Paper for 2024 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## (c) (-∞,0)∪(0,∞)                        (d) (-∞,∞)

This question is similar to Question-15 NCERT-Exemplar-MCQs

### Transcript

๐(๐ฅ) = ๐ฅ+|๐ฅ| = {โ(๐ฅ+๐ฅ, ๐ฅโฅ0@๐ฅโ๐ฅ, ๐ฅ <0)โค = {โ(2๐ฅ, ๐ฅโฅ0@0, ๐ฅ<0)โค Now, f(x) is a differentiable at x = 0 if LHD = RHD (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐ โ ๐))/๐ = (๐๐๐)โฌ(hโ0) (๐(0) โ ๐(0 โ โ))/โ = (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(โ๐))/๐ =(๐๐๐)โฌ(โโ0) (2(0) โ 0)/โ = (๐๐๐)โฌ(hโ0) 0/โ = ๐ (๐๐๐)โฌ(๐กโ๐) (๐(๐ + ๐) โ ๐(๐ ))/๐ = (๐๐๐)โฌ(hโ0) (๐(0 + โ) โ ๐(0))/โ = (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐))/๐ = (๐๐๐)โฌ(hโ0) (2โ โ 0)/โ = (๐๐๐)โฌ(hโ0) 2โ/โ = ๐ Hence, we can say that f(x) is differentiable on R โ {๐} or (โโ,๐)โช(๐,โ) So, the correct answer is (c)